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Quantum Programming

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Mathematics of Program Construction (MPC 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1837))

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Abstract

In this paper a programming language, qGCL, is presented for the expression of quantum algorithms. It contains the features required to program a ‘universal’ quantum computer (including initialisation and observation), has a formal semantics and body of laws, and provides a refinement calculus supporting the verification and derivation of programs against their specifications. A representative selection of quantum algorithms are expressed in the language and one of them is derived from its specification.

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References

  1. Baker, G.: http://www.ics.mq.edu.au/~gregb/q-gol

  2. Barenco, A., et al.: Elementary gates of quantum computation. Physical Review A 52(5), 3457–3467 (1995)

    Article  Google Scholar 

  3. Barenco, A.: A universal two-bit gate for quantum computation. Proc. R. Soc. Lond. A 449, 679–683 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  4. Boyer, M., Brassard, G., Hoyer, P., Tapp, A.: Tight bounds on quantum searching. In: Toffoli, T., Biaford, M., Lean, J. (eds.) Fourth Workshop on Physics and Computation, New England Complex System Institute, pp. 36–43 (1996)

    Google Scholar 

  5. Butler, M., Hartel, P.: Reasoning about Grover’s quantum search algorithm using probabilistic wp. University of Southampton technical report DSSETR- 98-10 (1998)

    Google Scholar 

  6. Cleve, R., Ekert, A., Macchiavello, C., Mosca, M.: Quantum algorithms revisited. Proc. R. Soc. Lond., A. 454, 339–354 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  7. Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A 400, 97–117 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  8. Deutsch, D.: Quantum computational networks. Proc. R. Soc. Lond. A 425, 73–90 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  9. Deutsch, D., Barenco, A., Ekert, A.: Universality in quantum computation. Proc. R. Soc. Lond. A 449, 669–677 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Deutsch, D., Jozsa, R.: Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. A 439, 553–558 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  11. Dijkstra, E.W.: A Discipline of Programming. Prentice-Hall International, Englewood Cliffs (1976)

    MATH  Google Scholar 

  12. Elitzur, A.C., Vaidman, L.: Quantum mechanical interaction-free measurements. Foundations of Physics 32(7), 987–997 (1993)

    Article  Google Scholar 

  13. Feynman, R.P.: The Feynman Lectures on Physics, vol. 3. Addison-Wesley, Reading (1964)

    Google Scholar 

  14. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th ACM STOC, pp. 212–219 (1996)

    Google Scholar 

  15. Gruska, J.: Quantum Computing. Advanced Topics in Computer Science. McGraw-Hill International, UK (1999)

    Google Scholar 

  16. Jifeng, H., Seidel, K., McIver, A.K.: Probabilistic models for the guarded command language. Science of Computer Programming 28, 171–192 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  17. Hoare He Jifeng, C.A.R.: The weakest prespecification. parts I and II. Fundamenta Informatica IX, 51–84 (1986)

    Google Scholar 

  18. Isham, C.J.: Lectures on Quantum Theory. Imperial College Press, London (1995)

    MATH  Google Scholar 

  19. Josza, R.: Characterising classes of functions computable by quantum parallelism. Proc. R. Soc. Lond. A 435, 563–574 (1991)

    Article  Google Scholar 

  20. Morgan, C.: Programming from Specifications, 2nd edn. Prentice-Hall International, Englewood Cliffs (1994)

    MATH  Google Scholar 

  21. Seidel, K., Morgan, C.C., McIver, A.K.: Probabilistic imperative programming: a rigorous approach (1996), Available at http://www.comlab.ox.ac.uk/oucl/research/areas/probs/bibliography.html

  22. Morgan, C., McIver, A., Seidel, K.: Annabelle McIver and Karen Seidel. Probabilistic predicate transformers. TOPLAS 18(3), 325–353 (1996)

    Google Scholar 

  23. Morgan, C., McIver, A.: pGCL: formal reasoning for random algorithms. South African Computer Journal 22, 14–27 (1999)

    Google Scholar 

  24. Morgan, C., McIver, A.K.: Demonic, angelic and unbounded probabilistic choices in sequential programs. To appear in Acta Informatica; see the site at [23]

    Google Scholar 

  25. Mosca, M., Ekert, A.: The hidden subgroup problem and eigenvalue estimation on a quantum computer. In: Williams, C.P. (ed.) QCQC 1998. LNCS, vol. 1509, p. 174. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  26. Ömer, B.: http://tph.tuwien.ac.at/oemer

  27. Peres, A.: Quantum Theory: Concepts and Methods. Kluwer Academic Publishers, Dordrecht (1998)

    Google Scholar 

  28. Schumacher, B.: Quantum coding. Physical Review A 51(4), 2738–2747 (1995)

    Article  MathSciNet  Google Scholar 

  29. Shor, P.W.: Algorithms for quantum computation: discrete log and factoring. In: Proceedings of the 35th IEEE FOCS, pp. 124–134 (1994)

    Google Scholar 

  30. Simon, D.R.: On the power of quantum computation. In: Proceedings of the 35th IEEE FOCS, pp. 116–123 (1994)

    Google Scholar 

  31. Williams, C.P., Clearwater, S.H.: Explorations in Quantum Computing. Springer, New York (1998)

    Google Scholar 

  32. Zuliani, P.: DPhil Thesis. Oxford University. (in preparation)

    Google Scholar 

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© 2000 Springer-Verlag Berlin Heidelberg

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Sanders, J.W., Zuliani, P. (2000). Quantum Programming. In: Backhouse, R., Oliveira, J.N. (eds) Mathematics of Program Construction. MPC 2000. Lecture Notes in Computer Science, vol 1837. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722010_6

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  • DOI: https://doi.org/10.1007/10722010_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67727-7

  • Online ISBN: 978-3-540-45025-2

  • eBook Packages: Springer Book Archive

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